Find the side length of a square with diagonals 18 cm long.

Answer:

[tex]\textsf{a)} \quad \overrightarrow{CA} =2\textbf{a}[/tex]

[tex]\textsf{b)} \quad \overrightarrow{AB} =\textbf{b}-\textbf{a}[/tex]

[tex]\textsf{c)} \quad \overrightarrow{BC} =-\textbf{a}-\textbf{b}[/tex]

Step-by-step explanation:

A parallelogram is a quadrilateral where opposite sides are equal in length and parallel to each other.  

The diagonals of a parallelogram are not equal in length, but they bisect each other (divide into two equal parts).

Therefore, if OA = a then CO = a.

Similarly, if OB = b then DO = b.

Part (a)

Express the vector CA in terms of a:

[tex]\begin{aligned}\overrightarrow{CA} &= \overrightarrow{CO} + \overrightarrow{OA}\\&=\textbf{a}+\textbf{a}\\&=2\textbf{a}\end{aligned}[/tex]

Part (b)

Express the vector AB in terms of a and b:

[tex]\begin{aligned}\overrightarrow{AB} &= \overrightarrow{AO} + \overrightarrow{OB}\\&= -\overrightarrow{OA} + \overrightarrow{OB}\\&= \overrightarrow{OB}-\overrightarrow{OA}\\&=\textbf{b}-\textbf{a}\end{aligned}[/tex]

Part (c)

Express the vector BC in terms of a and b:

[tex]\begin{aligned}\overrightarrow{BC} &= \overrightarrow{BO} + \overrightarrow{OC}\\&= -\overrightarrow{OB} - \overrightarrow{CO}\\&= -\overrightarrow{CO}-\overrightarrow{OB}\\&=-\textbf{a}-\textbf{b}\end{aligned}[/tex]

Answer:

a=x-89|4|-3<69

Step-by-step explanation:

Answer:

Step-by-step explanation:

His salary after 7 years would be $57000 per year

Answer:

Step-by-step explanation:

the answer for this question would be $57,000.

The number of shirts that Janice can buy without going over her limit is; 3 shirts

The number of shirts she can buy is denoted as s.

Cost of each shirt = $14

Cost of a pair of jeans = $32

She wants to spend less than $88.

Thus, the inequality that depicts this problem is;

14s + 32 < 88

Subtract 32 from both sides to get;

14s < 56

Divide both sides by 14 to get;

s < 4

Thus, maximum number of shirts will be 3 shirts

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Pedro weighs slightly more than Pablo.

It is the conversion of one unit to another unit with its standard conversion.

Examples:

1 hour = 60 minutes

1 minute = 60 seconds

1 km = 1000 m

We have,

Pedro weighs = 43 kg

Pablo weighs = 94 pounds.

Now,

1 kg = 2.205 pounds

Multiply 43 on both sides.

43 kg = 43 x 2.205 pounds

43 kg = 94.815 pounds

94.815 pounds > 94 pounds

We can see that Pedro weighs slightly more than Pablo.

Thus,

Pedro weighs slightly more than Pablo.

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The complete question in English.

Last week, Pedro and Pablo went to the doctor for a routine checkup. If Pedro weighs 43 kg and Pablo weighs 94 pounds, compare their weights to the same unit of measurement.

Who weights more?

Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To compare the temperatures of Location A and Location B, we need to convert the temperature of Location B from Celsius to Fahrenheit. We can use the formula:

°F = (°C × 9/5) + 32

Substituting the given temperature of Location B, we get:

°F = (29.3 × 9/5) + 32 = 84.74°F (rounded to two decimal places)

So, the average temperature of Location A is 85.3°F and the average temperature of Location B is 84.74°F (rounded to two decimal places).

Therefore, Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).

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Answer:

Step-by-step explanation:

Permutations and combinations are mathematical concepts that deal with counting the number of different arrangements or selections of objects from a set.

Permutations:

A permutation is an arrangement of objects in a specific order. For example, consider a set of three letters: A, B, and C. There are 3! = 6 possible permutations of these letters, which are ABC, ACB, BAC, BCA, CAB, and CBA. The notation "3!" is the factorial notation, which means 3 × 2 × 1.

Combinations:

A combination is a selection of objects, where the order does not matter. For example, consider a set of three letters: A, B, and C. There are 3 C 2 = 3 possible combinations of two letters from this set, which are AB, AC, and BC. The notation "3 C 2" is the combination notation, which means the number of ways to choose k objects from a set of n objects.

In summary, permutations deal with the arrangement of objects in a specific order, while combinations deal with the selection of objects without regard to the order.

Answer:

x > - 6

Step-by-step explanation:

[tex]\frac{x}{2}[/tex] > - 3 ( multiply both sides by 2 to clear the fraction )

x > - 6

The factored expression of (a-b) * 2 + 3(b-a)^2 is (-2 + 3(b - a))(b - a)

From the question, we have the following parameters that can be used in our computation:

(a-b)*z+3(b-a)^2

Express properly

So, we have

(a-b) * 2 + 3(b-a)^2

Rewrite as

-2(b - a) + 3(b - a)^2

Factor out b - a from the expression

So, we have

(-2 + 3(b - a))(b - a)

Hence, the factored expression is (-2 + 3(b - a))(b - a)

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Variance analysis is the quantitative investigation of the difference between actual and planned behavior. This analysis is used to maintain control over a business through the investigation of areas in which performance was unexpectedly poor.

Variance analysis is the study of deviations of actual behaviour versus forecasted or planned behaviour in budgeting or management accounting. This is essentially concerned with how the difference of actual and planned behaviors indicates how business performance is being impacted.

Comparing Budget with Actual: Variance analysis helps in managing the annual budgets by monitoring the budgeted figures and comparing it with the actual revenue/cost. In case of companies which are project or program driven, the financial data are evaluated at key intervals such as month close, quarter end, etc.

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Answer:

x= -177

Step-by-step explanation:

−13(x + 11) + 12x =-26

x=-177

The numeric value of the function when x = 0 is found replacing each instance of x by zero in the definition of the function.

If a graph is given, then the numeric value is given as the value of y when the function crosses the y-axis.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Supposing we have a function definition, then the numeric value at x = 0 is found replacing each instance of x by zero.

On graph, x = 0 is when the graph of the function touches or crosses the y-axis.

The problem is incomplete, hence the general procedure to obtain the numeric value at x = 0 was presented.

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The measure of each interior angle is 120 degrees.

In conclusion, the measure of each interior angle of a regular polygon with central angles measuring 60 degrees is 120 degrees.

The measure of each interior angle of a regular polygon with central angles measuring 60 degrees can be found using the formula (n-2)180/n, where n is the number of sides of the polygon.

First, we need to find the number of sides of the polygon. Since the measure of each central angle is 60 degrees, we can use the formula 360/n = 60 to find the number of sides.

Solving for n, we get: 360/n = 60 360 = 60n n = 360/60 n = 6 So the polygon has 6 sides.

Now we can use the formula (n-2)180/n to find the measure of each interior angle:

(6-2)180/6 = (4)180/6 = 720/6 = 120 degrees

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Answer:

The amount of time Jill trained this month is 125% of the amount of time she trained last month, which was 80 hours. To find the number of hours she trained this month, we can multiply 80 hours by 125%:

80 hours * 125% = 80 hours * 1.25 = 100 hours

So Jill trained for 100 hours this month.

Answer:

100hours

100 hours / 80 hours * 100% = 125%

Step-by-step explanation:

The amount of time Jill trained this month is 125% of the amount of time she trained last month, which was 80 hours. So, she trained for 125% of 80 hours = 100 hours.

To find this answer as a percentage, we can calculate what percentage of 80 hours 100 hours is:

100 hours / 80 hours * 100% = 125%

So Jill trained for 125% of the amount of time she trained last month.

If the given function is f(3/4), then evaluation of function (3/4) = 5/4.

What is expression ?

An expression is a mathematical phrase that can contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions, exponents, and other mathematical symbols.

Expressions can be used to represent a wide range of mathematical concepts, such as equations, inequalities, and formulas. They can be as simple as a single number or variable, or they can be more complex, involving multiple operations and variables.

What is function ?

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. In other words, a function is a rule or mapping that assigns a unique output to each input.

Functions can be expressed using a variety of mathematical expressions, such as algebraic formulas, graphs, and tables. They are used to model relationships between variables in many areas of mathematics, science, engineering, and other fields.

According t o given condition :

To find f(3/4), we simply substitute 3/4 in place of x in the given function f(x):

f(3/4) = 2(3/4) - 1/4

Simplifying the expression, we get:

f(3/4) = 6/4 - 1/4

f(3/4) = 5/4

Therefore, if the given function is f(3/4), then evaluation of function (3/4) = 5/4.

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The value of x is given as follows:

x = 30.

Similar triangles are triangles that share these two features presented as follows:

For the two similar triangles, we have that B and N are equivalent angles, hence they are congruent and the value of x is given as follows:

2x + 7 = 67

2x = 60

x = 60/2

x = 30.

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Answer:

40

Step-by-step explanation:

With MATLAB 's "t f" function, you may build a transfer function. A transfer function object is created by the "t f" function and can be used to manipulate transfer functions

So, you can create a transfer function with the aid of MATLAB's "t f" function. The "t f" function generates a transfer function object that can be used to manipulate transfer functions in a variety of ways, such as multiplying, adding, and inverting them. The MATLAB "t f" function can produce transfer functions using the following syntax. The numerator and denominator coefficients of the transfer function are "num" and "den", respectively and they are used to compute the system equation:  sys = t f(num, den). The coefficients of "num" and "den" can be visualised as vectors, with "s" serving as the Laplace variable and the coefficients as descending powers of "s." Consider using the transfer function equation below as an example to create

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The cost of each ticket is $34.17

To find the cost of each ticket, we need to divide the total cost of the tickets by the number of tickets.

In this case, the total cost of the tickets is $102.51 for three tickets.

So, to find the cost of one ticket,

We can divide $102.51 by 3:

Using the above as a guide, we have the following:

$102.51 ÷ 3 = $34.17

Hence, each ticket costs $34.17.

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In the given diagram, the measure of angle B, m ∠B, is 22°

From the question, we ae to calculate the measure of angle B

From the law of cosines, we can write that

cos B = (a² + c² - b²)/2ac

From the given diagram,

a = 6

b = 5

c = 10

Thus,

cos B = (6² + 10² - 5²)/2(6)(10)

cos B = (36 + 100 - 25)/120

cos B = 111/120

B = cos⁻¹(111/120)

B = 22.3316°

B ≈ 22°

Hence, m ∠B = 22°

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The required factor each polynomial by grouping are factored.

A polynomial is an algebraic expression in which the operators "+" and "-" are used to separate terms, and the exponents of the variables are consistently non-negative integers. Polynomials include, for instance, x² + x + 5, y² + 1, and 3x³ - 7x + 2.

1) [tex]x^3+4x^2+2x+8[/tex]

can be factored by grouping as:

[tex]x^3 + 2x + 4x^2 + 8[/tex]

= [tex]x(x^2+2) + 4(x^2+2)[/tex]

= [tex](x+4)(x^2+2)[/tex]

2) [tex]4b^3-6b^2+10b-15[/tex]

can be factored by grouping as:

[tex]2b^2(2b-3)+5(2b-3)[/tex]

=[tex](2b-3)(2b^2+5)[/tex]

3)[tex]2m^3+4m^2+6m+12[/tex]

can be factored by grouping as:

[tex]2m^2(m+2) + 6(m+2)[/tex]

= [tex](2m^2+6)(m+2)[/tex]

= [tex]2(m^2+3)(m+2)[/tex]

4) [tex]7r^3-35r^2+6r-30[/tex]

can be factored by grouping as:

[tex]7r^2(r-5)+6(r-5)[/tex]

=[tex](7r^2+6)(r-5)[/tex]

[tex]10a^3+4a^2+5a+2[/tex]

can be factored by grouping as:

[tex]2a^2(5a+2)+1(5a+2) = (2a^2+1)(5a+2)[/tex]

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Answer:

Step-by-step explanation:

The formula for the volume of a cone is given by:

V = (1/3)πr^2h

where V is the volume of the cone, r is the radius of the base, h is the height of the cone, and π is the mathematical constant pi (approximately equal to 3.14159).

Substituting the given values, we get:

471 = (1/3) x 13.4 x 5^2 x h

Multiplying both sides by 3 and dividing by 13.4 x 25, we get:

h = 471 x 3 / (13.4 x 25)

h ≈ 6.98 yards (rounded to two decimal places)

Therefore, the height of the cone is approximately 6.98 yards.

The solutions can be any rational number less than -20. They do not have to be integers.

Real numbers are the set of all rational and irrational numbers, which include numbers such as integers, fractions, decimals, square roots, and transcendental numbers like pi and e. Real numbers can be represented on a number line, where each point corresponds to a unique real number. The set of real numbers is denoted by the symbol R. Real numbers are used in various branches of mathematics, including algebra, calculus, and geometry, and have applications in various fields such as physics, engineering, and economics.

Given to the question: -

No, your choices are not correct.

The correct choices are:

There are infinite solutions.

Each solution is less than negative 20.

Each solution is a real number.

The solutions contain rational number values.

To explain further:

The inequality x < -20 means that any value of x that is less than -20 is a solution. There are an infinite number of values less than -20, so there are infinite solutions.

Each solution is less than -20. Therefore, each solution is negative.

The solutions can be any real number less than -20, so they can be positive, negative or zero, but they must be less than -20.

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Answer:

Let the weight of Train A be x tons. Then the weight of Train B is 537 - x tons. We know that the difference between their weights is 421 tons, so we can set up an equation to solve for x:

x - (537 - x) = 421

Expanding the right side:

x - 537 + x = 421

Combining like terms:

2x = 958

Dividing both sides by 2:

x = 479

So Train A weighs 479 tons and Train B weighs 537 - 479 = 58 tons.

Step-by-step explanation:

The product is ( 2) option (B)

( 0)

A scalar is a physical quantity that is completely defined by its magnitude. Dot Product: A dot product is the product of two vectors by taking the component of the second vector in the direction of the first vector. In the above diagram, there are two vectors A → and B → .

The scalar product is obtained by multiplying 2 by other value

2 × -1 = -2

2 × 0 = 0

therefore the scalar product is {2}

{0}

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The conversion rate for grams to tablespoons is 1 gram is equal to 0.2 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.50 grams is equal to 10 tablespoons."

This means that 50 grams is equal to 10 tablespoons. To calculate the value of 50 grams in tablespoons, we can use the following formula:50 grams x 0.2 tablespoons = 10 tablespoons.The value of 50 grams in tablespoons is 10 tablespoons.To convert from grams to tablespoons, the basic formula is to multiply the weight in grams by 0.2. This conversion is useful for converting small amounts of ingredients in recipes, as many recipes call for weights in grams rather than tablespoons. For example, if a recipe calls for 20 grams of butter, this would be equal to 4 tablespoons. To convert from tablespoons to grams, the basic formula is to multiply the weight in tablespoons by 5. This conversion is useful for converting larger amounts of ingredients in recipes, as many recipes call for weights in tablespoons rather than grams. For example, if a recipe calls for 8 tablespoons of sugar, this would be equal to 40 grams. To summarize, the value of 50 grams in tablespoons is 10 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.

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Answer:

Step-by-step explanation:

= 1/4 + 2/5

= 5/20 + 8/20

= 13/20

Answer: (9,8) A

Step-by-step explanation: how the mandle 10 30  6 150 144

The required speed of the object increase only one time.

We can see how far an object has moved over time by looking at a distance-time graph. The motion is faster when the graph is steeper. A horizontal line indicates that an object is at rest and not altering position. A downward sloping line indicates that the thing is going back to the beginning.

As we can see that upwards and downwards in the graph, which says about the increase and decrease in speed of the object.

First speed of object increase, then constant for some time.After that it decreases and then constant, at last it was decrease.

So, the speed of car is increase only one time.

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